GPS, Pseudo-Random Sequences, and the Weil Representation


Shamgar Gurevich

University of Wisconsin, Madison

Northeastern University

Thursday, March 28, 2013


Talk at 4:30 p.m. in 509 Lake Hall A

Tea at 4:00 p.m. in 544 Nightingale Hall


Abstract: I will explain how the digital part of the GPS (Global Positioning System) works. In particular, the role of pseudo-random sequences. These are sequences of N complex numbers S[0],S[1],,S[N-1] which behave as if they are random. I will explain a natural construction of such sequences using the Weil representation over Z/N. To prove the pseudo-randomness of the Weil sequences, I will use the Geometric Weil Representation. This is the l-adic sheaf realization of the Weil representation, which enables to introduce Weil II (Deligne's Theorem) techniques to explain the pseudo-randomness. The talk is based on joint projects with Fish (Math, Sydney), Hadani (Math, Austin), Sayeed (EE, Madison), Schwartz (CS, Berkeley), Sochen (Applied Math, Tel Aviv).

Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from Jonathan Weitsman.

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Posted: January 30, 2013    URL: